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A Comparative Study of Two Allen-Cahn Models for Immiscible $N$-Phase Flows by Using a Consistent and Conservative Lattice Boltzmann Method

A Comparative Study of Two Allen-Cahn Models for Immiscible $N$-Phase Flows by Using a Consistent and Conservative Lattice Boltzmann Method

Year:    2024

Author:    Chengjie Zhan, Xi Liu, Zhenhua Chai, Baochang Shi

Communications in Computational Physics, Vol. 36 (2024), Iss. 3 : pp. 850–876

Abstract

In this work, we conduct a detailed comparison between two second-order conservative Allen-Cahn (AC) models [Model A: Zheng et al., Phys. Rev. E 101, 0433202 (2020) and Model B: Mirjalili and Mani, J. Comput. Phys. 498, 112657 (2024)] for the immiscible $N$-phase flows. Mathematically, these two AC equations can be proved to be equivalent under some approximate conditions. However, the effects of these approximations are unclear from the theoretical point of view, and would be considered numerically. To this end, we propose a consistent and conservative lattice Boltzmann method for the AC models for $N$-phase flows, and present some numerical comparisons of accuracy and stability between these two AC models. The results show that both two AC models have good performances in accuracy, but the Model B is more stable for the realistic complex $N$-phase flows, although there is an adjustable parameter in the Model A.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2023-0228

Communications in Computational Physics, Vol. 36 (2024), Iss. 3 : pp. 850–876

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Model comparisons Allen-Cahn models $N$-phase flows lattice Boltzmann method.

Author Details

Chengjie Zhan

Xi Liu

Zhenhua Chai

Baochang Shi